\documentclass[twoside,11pt]{article}
\usepackage{amsmath,amssymb,amsthm}
\usepackage[vlined,algoruled,titlenumbered,noend]{algorithm2e}
\usepackage{epsfig,subfigure,graphicx}
\begin{document}
\begin{align*}
& P(d' = 1 |x_1,x_2,d)  = \begin{cases}
0.7\\
0.3\\
\end{cases} 
\\
& P(x'_1 |x_1,x_2,d) = \delta \left(  x'_1 - \begin{cases}
d  \wedge (x_1 + a_1 + x_2 - 150 \leq C) : & x_1 + a_1 - 150 \\
d  \wedge (x_1 + a_1 + x_2 - 150 \geq C) : & x_1 - 150  \\
\neg d \wedge (x_1 + a_1 +  x_2 - 50 \leq C): & x_1 + a_1 - 50    \\
\neg d \wedge (x_1 + a_1 +  x_2 - 50 \geq C): & x_1 - 50    \\
\end{cases}  \right)
\\
& P(x'_2 |x_1,x_2,d) = \delta \left(  x'_2 - \begin{cases}
d  \wedge (x_2 + a_2 + x_1 - 150 \leq C) : & x_2 + a_2 - 150 \\
d  \wedge (x_2 + a_2 + x_1 - 150 \geq C) : & x_2 - 150  \\
\neg d \wedge (x_2 + a_2 +  x_1 - 50 \leq C): & x_2 + a_2 - 50    \\
\neg d \wedge (x_2 + a_2 +  x_1 - 50 \geq C): & x_2 - 50    \\
\end{cases}  \right)
\\
& R(x_1,x_2,d,a_1,a_2)  = \begin{cases}
d \wedge (x_1 + x_2  \leq 200) \wedge (x_1 \geq 150) \wedge (x_2 \geq 150) : & 300 - 0.5*a_1 - 0.5*a_2\\
d \wedge (x_1 + x_2  \leq 200) \wedge (x_1 \geq 150) \wedge (x_2 \leq 150) : & 150 + x_2 - 0.5*a_1 - 0.5*a_2\\
d \wedge (x_1 + x_2  \leq 200) \wedge (x_1 \leq 150) \wedge (x_2 \geq 150) : & 150 + x_1 - 0.5*a_1 - 0.5*a_2\\
d \wedge (x_1 + x_2  \leq 200) \wedge (x_1 \leq 150) \wedge (x_2 \leq 150) : & x_1 + x_2 - 0.5*a_1 - 0.5*a_2\\
\neg d \wedge (x_1 + x_2  \leq 200) \wedge (x_1 \geq 50) \wedge (x_2 \geq 50) : & 100 - 0.5*a_1 - 0.5*a_2\\
\neg d \wedge (x_1 + x_2  \leq 200) \wedge (x_1 \geq 50) \wedge (x_2 \leq 50) : & 50 + x_2 - 0.5*a_1 - 0.5*a_2\\
\neg d \wedge (x_1 + x_2  \leq 200) \wedge (x_1 \leq 50) \wedge (x_2 \geq 50) : & 50 + x_1 - 0.5*a_1 - 0.5*a_2\\
\neg d \wedge (x_1 + x_2  \leq 200) \wedge (x_1 \leq 50) \wedge (x_2 \leq 50) : & x_1 + x_2 - 0.5*a_1 - 0.5*a_2\\
(x_1 + x_2  \geq 200): -300 - 0.5*a_1 - 0.4 *a_2\\
\end{cases} \label{rew_inv}
\end{align*}

\end{document}